Damage analysis of tetragonal perovskite structure ceramics implicated by asymptotic field solutions and boundary conditions

Cracking of ceramics with tetragonal perovskite grain structure is known to appear at different sites and scale level. The multiscale character of damage depends on the combined effects of electromechanical coupling, prevailing physical parameters and boundary conditions. These detail features are exhibited by application of the energy density criterion with judicious use of the mode I asymptotic and full field solution in the range of r/a = 10(-4) to 10(-2) where r and a are, respectively, the distance to the crack tip and half crack length. Very close to the stationary crack tip, bifurcation is predicted resembling the dislocation emission behavior invoked in the molecular dynamics model. At the macroscopic scale, crack growth is predicted to occur straight ahead with two yield zones to the sides. A multiscale feature of crack tip damage is provided for the first time. Numerical values of the relative distances and bifurcation angles are reported for the PZT-4 ceramic subjected to different electric field to applied stress ratio and boundary conditions that consist of the specification of electric field/mechanical stress, electric displacement/mechanical strain, and mixed conditions. To be emphasized is that the multiscale character of damage in piezoceramics does not appear in general. It occurs only for specific combinations of the external and internal field parameters, elastic/piezoelectric/dielectric constants and specified boundary conditions. (C) 2002 Published by Elsevier Science Ltd.

On the computation of space-time correlations by large-eddy simulation

The effect of subgrid-scale (SGS) modeling on velocity (space-) time correlations is investigated in decaying isotropic turbulence. The performance of several SGS models is evaluated, which shows superiority of the dynamic Smagorinsky model used in conjunction with the multiscale large-eddy simulation (LES) procedure. Compared to the results of direct numerical simulation, LES is shown to underpredict the (un-normalized) correlation magnitude and slightly overpredict the decorrelation time scales. This can lead to inaccurate solutions in applications such as aeroacoustics. The underprediction of correlation functions is particularly severe for higher wavenumber modes which are swept by the most energetic modes. The classic sweeping hypothesis for stationary turbulence is generalized for decaying turbulence and used to analyze the observed discrepancies. Based on this analysis, the time correlations are determined by the wavenumber energy spectra and the sweeping velocity, which is the square root of the total energy. Hence, an accurate prediction of the instantaneous energy spectra is most critical to the accurate computation of time correlations. (C) 2004 American Institute of Physics.

Energy principle of ferroelectric ceramics and single domain mechanical model

Many physical experiments have shown that the domain switching in a ferroelectric material is a complicated evolution process of the domain wall with the variation of stress and electric field. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of ferroelectric ceramic and used to study the nonlinear constitutive behavior of ferroelectric body in this paper. The principle of stationary total energy is put forward in which the basic unknown quantities are the displacement u (i) , electric displacement D (i) and volume fraction rho (I) of the domain switching for the variant I. Mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion. On the basis of the domain switching criterion, a set of linear algebraic equations for the volume fraction rho (I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. Then a single domain mechanical model is proposed in this paper. The poled ferroelectric specimen is considered as a transversely isotropic single domain. By using the partial experimental results, the hardening relation between the driving force of domain switching and the volume fraction of domain switching can be calibrated. Then the electromechanical response can be calculated on the basis of the calibrated hardening relation. The results involve the electric butterfly shaped curves of axial strain versus axial electric field, the hysteresis loops of electric displacement versus electric filed and the evolution process of the domain switching in the ferroelectric specimens under uniaxial coupled stress and electric field loading. The present theoretic prediction agrees reasonably with the experimental results given by Lynch.

A novel oblique detonation structure and its stability

Oblique detonation structures induced by the wedge in the supersonic combustible gas mixtures are simulated numerically. The results show that the stationary oblique detonation structures are influenced by the gas flow Mach number, and a novel critical oblique detonation structure, which is characterized by a more complicated wave system, appears in the low Mach number cases. By introducing the inflow disturbance, its nonstationary evolution process is illustrated and its stability is verified.

Análisis de costos de producción ganadera según el tamaño de los hatos

Este estudio esta basado en una encuesta de 160 explotaciones ganaderas efectuadas por la unidad de análisis sectorial del Comité Nacional Agropecuario. Las explotaciones fueron agrupadas en cinco categorías según el tamaño de los hatos que corresponden a explotaciones con menos de 10 cabezas, 10 a 50, 51 a 100, 101 a 500 y mas de 500 cabezas. Los datos obtenidos se analizaron para determinar si había alguna economía de escala y eficiencia adicional al aumentar el tamaño de los hatos ganaderos. Los resultados obtenidos indican que existe una economía de escala bien definida en el costo de la mano de obra y en el numero de días-hombre empleados por cabeza. Las explotaciones de mayor tamaño también tienen tierras y pastos de calidad superior, alquilan menos tierras para su ganado y usan mas asistencia técnica. Los otros costos en que incurre el productor no tiene una tendencia definida. Los costos totales por categoría de tamaño no muestran una tendencia pero los ingresos brutos, beneficios netos y retornos a la inversión son generalmente mayores en las explotaciones de mayor tamaño lo que indica que estas hacen un uso mas eficiente de sus recursos. Las explotaciones de mayor tamaño tienen mas recursos propios y mayor capacidad de pago mientras que las explotaciones mas pequeñas que tienen que adquirir de terceros una mayor proporción de los recursos usados en la producción tienen menor capacidad de pago.

On the topological bifurcation of flows around a rotating circular cylinder

Flow fields around a rotating circular cylinder in a uniform stream are computed using a low dimensional Galerkin method. Results show that the formation of a Fopple vortex pair behind a stationary circular cylinder is caused by the structural instability in the vicinity of the saddle located at the rear of the cylinder. For rotating cylinder a bifurcation diagram with the consideration of two parameters, Reynolds number Re and rotation parameter a, is built by a kinematic analysis of the steady flow fields.

Numerical study of bifurcation solutions of spherical Taylor-Couette flow

The steady bifurcation flows in a spherical gap (gap ratio sigma=0.18) with rotating inner and stationary outer spheres are simulated numerically for Re(c1)less than or equal to Re less than or equal to 1 500 by solving steady axisymmetric incompressible Navier-Stokes equations using a finite difference method. The simulation shows that there exist two steady stable flows with 1 or 2 vortices per hemisphere for 775 less than or equal to Re less than or equal to 1 220 and three steady stable flows with 0, 1, or 2 vortices for 1 220

Hopf bifurcation in wakes behind a rotating and translating circular cylinder

A low-dimensional Galerkin method, initiated by Noack and Eckelmann [Physica D 56, 151 (1992)], for the prediction of the flow field around a stationary two-dimensional circular cylinder in a uniform stream at low Reynolds number is generalized to the case of a rotating and translating cylinder. The Hopf bifurcation describing the transition from steady to time-periodic solution is investigated. A curve indicating the transitional boundary is given in the two-dimensional parameter plane of Reynolds number Re and rotating parameter alpha. Our results show that rotation may delay the onset of vortex street and decrease the vortex-shedding frequency. (C) 1996 American Institute of Physics.

Higher-order analysis of crack tip fields in elastic power-law hardening materials

A HIGHER-ORDER asymptotic analysis of a stationary crack in an elastic power-law hardening material has been carried out for plane strain, Mode 1. The extent to which elasticity affects the near-tip fields is determined by the strain hardening exponent n. Five terms in the asymptotic series for the stresses have been derived for n = 3. However, only three amplitudes can be independently prescribed. These are K1, K2 and K5 corresponding to amplitudes of the first-, second- and fifth-order terms. Four terms in the asymptotic series have been obtained for n = 5, 7 and 10; in these cases, the independent amplitudes are K1, K2 and K4. It is found that appropriate choices of K2 and K4 can reproduce near-tip fields representative of a broad range of crack tip constraints in moderate and low hardening materials. Indeed, fields characterized by distinctly different stress triaxiality levels (established by finite element analysis) have been matched by the asymptotic series. The zone of dominance of the asymptotic series extends over distances of about 10 crack openings ahead of the crack tip encompassing length scales that are microstructurally significant. Furthermore, the higher-order terms collectively describe a spatially uniform hydrostatic stress field (of adjustable magnitude) ahead of the crack. Our results lend support to a suggestion that J and a measure of near-tip stress triaxiality can describe the full range of near-tip states.

Nonequilibrium statistical mechanics of two-dimensional turbulence

The vorticity dynamics of two-dimensional turbulence are investigated analytically, applying the method of Qian (1983). The vorticity equation and its Fourier transform are presented; a set of modal parameters and a modal dynamic equation are derived; and the corresponding Liouville equation for the probability distribution in phase space is solved using a Langevin/Fokker-Planck approach to obtain integral equations for the enstrophy and for the dynamic damping coefficient eta. The equilibrium spectrum for inviscid flow is found to be a stationary solution of the enstrophy equation, and the inertial-range spectrum is determined by introducing a localization factor in the two integral equations and evaluating the localized versions numerically.

Variational approach to the closure problem of turbulence theory

A new method is proposed to solve the closure problem of turbulence theory and to drive the Kolmogorov law in an Eulerian framework. Instead of using complex Fourier components of velocity field as modal parameters, a complete set of independent real parameters and dynamic equations are worked out to describe the dynamic states of a turbulence. Classical statistical mechanics is used to study the statistical behavior of the turbulence. An approximate stationary solution of the Liouville equation is obtained by a perturbation method based on a Langevin-Fokker-Planck (LFP) model. The dynamic damping coefficient eta of the LFP model is treated as an optimum control parameter to minimize the error of the perturbation solution; this leads to a convergent integral equation for eta to replace the divergent response equation of Kraichnan's direct-interaction (DI) approximation, thereby solving the closure problem without appealing to a Lagrangian formulation. The Kolmogorov constant Ko is evaluated numerically, obtaining Ko = 1.2, which is compatible with the experimental data given by Gibson and Schwartz, (1963).

The wave model of mesothermal plasma near wakes and Korteweg-de Vries equation

The stationary two-dimensional (x, z) near wakes behind a flat-based projectile which moves at a constant mesothermal speed (V∞) along a z-axis in a rarefied, fully ionized, plasma is studied using the wave model previously proposed by one of the authors (VCL). One-fluid theory is used to depict the free expansion of ambient plasma into the vacuum produced behind a fast-moving projectile. This nonstationary, one-dimensional (x, t) flow which is approximated by the K-dV equation can be transformed, through substitution, t=z/V∞, into a stationary two-dimensional (x, z) near wake flow seen by an observer moving with the body velocity (V∞). The initial value problem of the K-dV equation in (x, t) variables is solved by a specially devised numerical method. Comparisons of the present numerical solution for the asymptotically small and large times with available analytical solutions are made and found in satisfactory agreements.

Why Economists Reject Long-Term Fisheries Management Plans?

Most fisheries agencies conduct biological and economic assessments independently. This independent conduct may lead to situations in which economists reject management plans proposed by biologists. The objective of this study is to show how to find optimal strategies that may satisfy biologists and economists' conditions. In particular we characterize optimal fishing trajectories that maximize the present value of a discounted economic indicator taking into account the age-structure of the population as in stock assessment methodologies. This approach is applied to the Northern Stock of Hake. Our main empirical findings are: i) Optimal policy may be far away from any of the classical scenarios proposed by biologists, ii) The more the future is discounted, the higher the likelihood of finding contradictions among scenarios proposed by biologists and conclusions from economic analysis, iii) Optimal management reduces the risk of the stock falling under precautionary levels, especially if the future is not discounted to much, and iv) Optimal stationary fishing rate may be very different depending on the economic indicator used as reference.

Flood of September 20-23, 1969 in the Gadsden County area, Florida

The center of low pressure of a tropical disturbance which moved northward in the Gulf of Mexico, reached land between Panama City and Port St. Joe, Florida, on September 20, 1969. This system was nearly stationary for 48 hours producing heavy rainfall in the Quincy-Havana area, 70-80 miles northeast of the center. Rainfall associated with the tropical disturbance exceeded 20 inches over a part of Gadsden County, Florida, during September 20 through 23, 1969, and the maximum rainfall of record occurred at Quincy with 10.87 inches during a 6-hour period on September 21. The 48-hour maximum of 17.71 inches exceeded the 1 in 100-year probability of 16 inches for a 7-day period. The previous maximum rainfall of record at Quincy (more than 12 inches) was on September 14-15, 1924. The characteristics of this historical storm were similar in path and effect to the September 1969 tropical disturbance. Peak runoff from a 1.4-square mile area near Midway, Florida, was 1,540 cfs (cubic feet per second) per square mile. A peak discharge of 45,600 cfs on September 22 at the gaging station on the Little River near Quincy exceeded the previous peak of 25,400 cfs which occurred on December 4, 1964. The peak discharge of 89,400 cfs at Ochlockonee River near Bloxham exceeded the April 1948 peak of 50,200 cfs, which was the previous maximum of record, by 1.8 times. Many flood-measurement sites had peak discharges in excess of that of a 50-year flood. Nearly $200,000 was spent on emergency repairs to roads. An additional $520,000 in contractual work was required to replace four bridges that were destroyed. Agricultural losses were estimated at $1,000,000. (44 page document)

Parámetros de contaminación y normativa en colectores urbanos

[ES] La contaminación por aguas residuales urbanas es uno de los problemas de mayor importancia para mantener un nivel de calidad aceptable del agua, debido al número elevado de fuentes, a la participación de la contaminación difusa y a la elevada concentración de materia orgánica. La normativa legal plantea unos límites eflDidos, pero no se han realizado campañas de seguimiento de forma suficiente para su comprobación, particularmente en estiaje. El problema se complica por la diversidad apreciable que se observa y la necesidad de dar significación estadística a las conclusiones. En este trabajo, junto a un análisis del seguimiento de una docena de parámetros en diversos colectores de aguas residuales de una zona urbana, se pretende eparar/advertir la dificultad que presenta cada uno de eUos para el cumplimiento legal en relación con las caraterísticas de las fuentes de procedencia y la situación estacional durante el análisis. Además, se pretende buscar de una forma incial las posibles relaciones que se presentan entre las variaciones simultáneas de dichos parámetros. Algunos de eUos muestran una relación clara por lo que podría establecerse alguna dependencia funcional, mientras que en otros casos el problema resulta excesivamente complejo por la necesidad de disponer de más información para Uegar a establecer alguna relación.